In PCT applications WO200930840 and WO200930841, Applicant's Company described graft polymers obtained from reaction between polymers, in particular between thiol derivatives and copolymers based on conjugated diene units and aromatic monovinyl hydrocarbon units. The grafting reaction of the thiol derivatives on the polymers is described on page 13 lines 26 to 29 in the case of application WO200930840 and on page 13 lines 7 to 10 in the case of application WO200930841. The grafting reaction takes place in a reactor, under a nitrogen atmosphere, in the presence of a solvent such as toluene, at a temperature of 90° C., with stirring, for a duration of 3 to 4 hours, in the presence of a polymer, a thiol derivative that performs the role of graft and a radical initiator such as azobisisobutyronitrile (AlBN).